Move First, Commit Later: Selective LiDAR-to-BIM Global Initialization by Verifying Proposals Against Competing Explanations

The gist: Global LiDAR-to-BIM initialization must place a robot within an as-designed building model without a prior pose, and this work presents Move First, Commit Later, a selective layer that treats a registration front-end as an evidence source and decides whether to commit.

Move First, Commit Later Mechanism

The proposed method is designed to treat the registration front-end as an evidence source and decide whether to commit The layer maps each submap’s candidates to a common anchor BTL in SE(2), aggregates a top-1 consensus Bm that is invariant to non-champion multiplicity, uses topology only as a binary feasibility gate, and repeatedly emits a typed decision—COMMIT, DEFER, or AMBIGUOUS(τ)—as the robot moves This turns global initialization from a one-shot registration decision into a sequential, evidencedriven decision process.

Consensus and Decision States

The system utilizes three distinct decision states to manage uncertainty: DEFER, AMBIGUOUS(τ), or COMMIT> DEFER denotes that evidence is not yet informative and motion may provide what is missing AMBIGUOUS denotes evidence saturated on an unresolvable equivalence class rather than a unique anchor, reporting the geometric form of non-identifiability rather than only a scalar score COMMIT requires three conditions: saturated evidence (the mapped trajectory spans at least two distinct rooms), a feasible winner, and decisive consensus.

Consensus Immune to Non-Champion Multiplicity

Contribution C2 introduces a top-1 consensus statistic Bm over common SE(2) anchors, where each submap contributes only its highest-scoring candidate. This ensures Bm is invariant to non-champion multiplicity because it counts champions rather than support, and cannot be inflated by head-count as support. Proposition 1 gives a dichotomy: in non-coherent layouts, the margin grows with the number of submaps; in exactly symmetric layouts, the true anchor is non-identifiable over a symmetry orbit, and the correct output is AMBIGUOUS.

Topology as a Physical-Realizability Gate

Topology serves only as a binary feasibility gate, rejecting physically impossible candidates without ranking feasible ones. The gate tests whether the mapped trajectory is physically realizable by checking for free-space validity, room membership, and inter-room adjacency. This gate precedes Bm computation so that consensus is computed only over survivors and cannot be contaminated by infeasible hypotheses.

Symmetry Characterization and Commitment Timing

The period τ appears only in the coherent AMBIGUOUS state and is a detected output, not an input. The layer synthesizes shifted anchors Aτ = T⋆ + nτ for n ∈ ±1,..., ±nmax to re-test each through the gate. This synthesis can veto an alias absent from the candidate set under exact symmetry, and AMBIGUOUS(τ) transitions to COMMIT after motion renders shifted anchors infeasible.

Empirical Validation

In real-world testing, the layer commits correctly in every tested trajectory-scale configuration and otherwise abstains with a typed state, whereas forced-choice policies on the same front-end select wrong rooms in most cases. The layer achieves full correct coverage with mean commit window 5.8, earlier than support (18.2) and confidence (10.7), confirming that the decision criterion, rather than longer waiting, drives correctness.

Simulation Results

In controlled extreme symmetry simulations, the layer remains AMBIGUOUS through the symmetric interior and commits only at k=12 after the robot encounters the sealed wall and consensus becomes decisive. The detected period remains within 0.09 m of the true 7.30 m pitch, with mean absolute error 0.04 m over clean coherent detections.

Limitations and Future Work

The lattice detector handles only translational symmetry; rotational and mirror symmetries remain future work. The consensus is immune to non-champion multiplicity but not to systematic top-1 bias, and the evaluation covers one building, three rooms, two trajectories, and one front-end.

Conclusion

In this paper, we presented a selective LiDAR-to-BIM initialization layer that decides whether to commit an anchor rather than forcing a best guess. It aggregates a top-1 consensus over multi-submap SE(2) anchors—immune to nonchampion multiplicity—uses topology only as a feasibility gate, and reports a typed abstention naming the period τ for translational lattices. Under the evaluated conditions, it commits in identifiable cases and abstains auditably when the geometry is non-identifiable, avoiding the forced-choice failures seen in the real building and exhibiting the AMBIGUOUS→COMMIT transition when motion breaks symmetry in simulation. The components address distinct failures: consensus resolves uniqueness, the gate removes infeasible candidates, and the periodic-alias probe protects the symmetric regime examined in Section IV-B.

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The gist: Global LiDAR-to-BIM initialization must place a robot within an as-designed building model without a prior pose, and this work presents Move First, Commit Later, a selective layer that treats a registration front-end as an evidence source and decides whether to commit.

How it works

The proposed method is designed to treat the registration front-end as an evidence source and decide whether to commit The layer maps each submap’s candidates to a common anchor BTL in SE(2), aggregates a top-1 consensus Bm that is invariant to non-champion multiplicity, uses topology only as a binary feasibility gate, and repeatedly emits a typed decision—COMMIT, DEFER, or AMBIGUOUS(τ)—as the robot moves.

1. Bold header: Selective Initialization Layer for LiDAR-to-BIM Registration

This layer transforms global initialization from a one-shot registration decision into a sequential, evidencedriven decision process by employing three typed states: COMMIT, DEFER, or AMBIGUOUS(τ). This allows the system to report the geometric form of non-identifiability rather than only a scalar confidence, specifically identifying translational ambiguities as a translational τ-lattice under coherent symmetry.

2. Bold header: Consensus Immune to Non-Champion Multiplicity

The system computes a consensus statistic Bm that is immune to non-champion multiplicity—the sense in which it is density-immune—and cannot be inflated by head-count as support-style counting can. This ensures the true anchor is identified even when multiple submaps match an alias, as the method counts champions, not support, preventing aliases from dominating the consensus based on candidate volume.

3. Bold header: Symmetry-Aware Commitment Decision

The decision machine implements a reversible state transition: symmetry-breaking motion upgrades AMBIGUOUS to COMMIT. This means the robot can actively seek out symmetry-breaking evidence to resolve an ambiguity, rather than being trapped by it, directly realizing the paper's core premise of Commit Later.

4. Bold header: Topological Feasibility Gate

Topology is used solely as a constraint: The BIM serves two roles: its geometry (walls and corners) drives registration, whereas its coarse layout—room extents and an occupancy grid—drives the gate. This gate ensures that candidates are only admitted if they are physically realizable, rejecting aliases whose trajectories jump between non-adjacent rooms while allowing legitimate revisits.

5. Bold header: Period Detection for Translational Lattices

When in the AMBIGUOUS state, the system actively detects symmetry by testing pairwise differences against a lattice hypothesis to estimate the period τ of translational ambiguity. This provides an auditable geometric statement about the structure, rather than just a score, which is crucial for understanding repetitive environments.

6. Bold header: Adaptive Commitment Timing

The system achieves correctness by adapting its decision based on evidence accumulation: commit timing adapts to the rate at which evidence collapses. By comparing its performance against forced-choice policies like support and confidence, the system demonstrates that correctness follows from champion rendezvous, not accumulated candidate count, leading to commits earlier than waiting strategies.